Does cloth armour have to be obviously padded armour like a ‘gambeson’ or would multiple layers of thick clothing count?

When it comes to physically representing cloth armour, there does need to be a distinction between normal clothes and the cloth armour. The core rules document give a few examples of lightweight armour from history.

A gambeson would not necessarily need to be worn as the top layer of costume, but you will be needed to point it out if a referee suspects “shenanigans” when a mage is taking a physical beating.